Hook lengths and 3-cores
| dc.creator | Han, Guo-Niu | |
| dc.creator | Ono, Ken | |
| dc.date | 2008-05-16 | |
| dc.date.accessioned | 2026-07-07T09:39:22Z | |
| dc.date.available | 2026-07-07T09:39:22Z | |
| dc.description | Recently, the first author generalized a formula of Nekrasov and Okounkov which gives a combinatorial formula, in terms of hook lengths of partitions, for the coefficients of certain power series. In the course of this investigation, he conjectured that $A000731(n)=0$ if and only if $A033687(n)=0$. The numbers $A000731(n)$ are given in terms of hook lengths of partitions, while $A033687(n)$ equals the number of 3-core partitions of $n$. Here we prove this conjecture. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/0805.2461 | |
| dc.identifier | http://arxiv.org/abs/0805.2461 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161147 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.title | Hook lengths and 3-cores | |
| dc.type | text |